Lectures related to Polynomials: Theory and Applications

Polynomials: Definitions and Operations

Covers the definition and operations of polynomials, including addition and multiplication, degree, coefficients, and their role in algebraic systems.

Polynomials on a Field: Basics and Operations

Introduces the basics of polynomials on a field, focusing on definitions, operations, and properties.

Digital Derivation: Evaluation and Formulas

Explores digital derivation, function evaluation, and polynomial approximations for accurate measurements and evaluations.

Differentiable Functions and Lagrange Multipliers

Covers differentiable functions, extreme points, and the Lagrange multiplier method for optimization.

Real Functions: Definitions and Properties

Explores real functions, covering parity, periodicity, and polynomial functions.

Mathematics: Analysis and Algebra Overview

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

Limits & Continuity: Analysis 1

Explores limits, continuity, and function compositions in mathematics.

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Vector Spaces: Definitions and Applications

Introduces vector spaces, subspaces, linear maps, and evaluation maps, with examples and exercises for better comprehension.

Advanced Counting: Linear Homogeneous Recurrence Relations and Generating Functions

Explores solving linear homogeneous recurrence relations and generating functions for sequence formulas.

Taylor's Formula: Developments and Applications

Explores Taylor's formula, polynomials, functions, and series applications.

Differential Equations: Implicit Function Theorem

Explores the implicit function theorem and Taylor polynomials in differential equations.

Vector Spaces: Properties and Examples

Explores vector spaces, focusing on properties, examples, and subspaces within a practical exercise on polynomials.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Linear Algebra: Abstract Concepts

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

Calculus Foundations: Taylor Series and Integrals

Introduces calculus concepts, focusing on Taylor series and integrals, including their applications and significance in mathematical analysis.

Fundamental Theorem of Calculus: Integrals and Primitives

Explains the Fundamental Theorem of Calculus, focusing on integrals and their relationship with primitives.

Linear Transformations: Polynomials and Bases

Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Linear Combinations and Vector Spaces

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Differential Equations: Methods and Solutions

Discusses methods for solving first-order linear differential equations, focusing on separation of variables and the integrating factor method.